I presume you mean more than three shots in one go. This is called continuous or burst mode in other cameras, and is dependent on several things.

The speed that the data is written to the memory card, the size of the images being shot and the design of the camera.

Often, the number of shots a camera can take in this mode is referred to in frames per second (FPS). Depending on the factors mentioned above, the top end dSLRs can achieve machine gun speeds of 10 FPS, and the average dSLR might do 3. How long the camera can keep this up is mostly influenced by the speed that the contents of the buffer can be written to the memory, but it is fair to say that the maximum FPS will only be achieved for a fairly short time, then the speed will drop to a slower speed that is then maintained until the memory is filled or the battery goes flat! Some cameras may stop taking pictures if the buffer is full and it has to wait for some more space to be made by dumping the images onto the memory card. This sounds like what is happening to you.

The specification on the web-site you have linked to does not mention any of this information, but a search of the Kodak knowledge base found this:

Burst mode: First burst up to 2 pictures; Last burst up to 2 pictures; both @ approx. 2 fps (Exposure, focus, and white balance executed for first shot only.)

I also found another web-site that said the burst mode will give three pictures.

So it would appear that your camera is doing what it was designed to do, and you will not be able to get more that three pictures in one go.